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A Very Grand Challenge for the Science of Climate Prediction Tim Palmer European Centre for Medium-Range Weather Forecasts and University of Oxford. There are essentially two types of climate model Idealised models eg. ..or (idealised barotropic vorticity equation). advection. orography. - PowerPoint PPT Presentation
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A Very Grand Challenge for the Science of Climate
Prediction
Tim Palmer
European Centre for Medium-Range Weather Forecasts
and
University of Oxford
There are essentially two types of climate model
1.Idealised models eg
4sun earth(1 ) 4A F T
2 2 2 *, , ( ) 0J f J h Ct
..or (idealised barotropic vorticity equation)
advection orography “equator-pole temperature gradient”
*1 3 1 1
2 1 3 2
3 1 2 1 3
( )
-( - )
-( - ) -
x x C x x
x x x Cx
x x x x Cx
Charney DeVore, 1979
Westerly/block flow regimes as multiple equlibria
2. “Ab initio” climate models eg based on
where basic weather is modelled explicitly from first principles.
2. pt
u u g u
Atmosphere Atmosphere Atmosphere Atmosphere Atmosphere Atmosphere
Land surfaceLand surfaceLand surfaceLand surfaceLand surface
Ocean & sea-ice Ocean & sea-ice Ocean & sea-ice Ocean & sea-ice
Sulphateaerosol
Sulphateaerosol
Sulphateaerosol
Non-sulphateaerosol
Non-sulphateaerosol
Carbon cycle Carbon cycle
Atmosphericchemistry
Ocean & sea-icemodel
Sulphurcycle model
Non-sulphateaerosols
Carboncycle model
Land carboncycle model
Ocean carboncycle model
Atmosphericchemistry
Atmosphericchemistry
Off-linemodeldevelopment
Strengthening coloursdenote improvementsin models
1975 1985 1992 1997
The
Met
.Offi
ce H
adle
y C
entr
e
Towards the Comprehensive Climate Model1970 2000
“Ab initio” models are important if we are to have confidence in predictions of global warming. Eg
4sun earth(1 ) 4A F T
Albedo depends on cloud cover, ice cover etc. Cannot be specified a priori, but depends on dynamics
IPCC AR4
Ab initio models are also needed, eg to guide adaptation strategies…
Will blocking become more prevalent under climate change…more reservoirs, national water grid etc…..??
…and, increasingly, to assess regional impacts of climate geoengineering proposals
Permanent El Nino, shutoff in monsoons…..????
Standard paradigm (20th Century vintage):
•Mathematicians (the academic community more generally) develop the idealised, mathematically tractable, models for improved understanding
•Software engineers in meteorological institutes develop the “brute force” ab initio models for quantitative predictions
I think this paradigm is outdated. In this lecture I wish to promote a new paradigm for the 21st Century
Standard ansatz for “ab initio” weather/climate models
Deterministic local bulk-formula parametrisation
Increasing scale
;nP X
Eg momentum“transport” by:
•Turbulent eddies in boundary layer
•Orographic gravity wave drag.
•Convective clouds
1X 2X 3X nX... ...
2. pt
u u g uEg
Standard bulk-formula parametrisation assumes the existence of a large ensemble of eg convective cloud systems within a grid box, in quasi-equlilibrium with the
large-scale flow.
Similar considerations for other parametrised processes, eg orographic gravity wave drag
Wavenumber spectra of zonal and meridional velocity composited from three groups of flight segments of different lengths. The three types of symbols show results from each group. The straight lines indicate slopes of –3 and –5/3. The meridional wind spectra are shifted one decade to the right.(after Nastrom et al, 1984).
Parametrisations motivated by statistical mechanics (eg molecular diffusion), but…
…there is no scale separation between resolved and unresolved scales at NWP truncations (eg
convection, orography)
Calculate exact PDF of sub-grid temperature tendencies in a coarse-grained (50km) grid box based on output from a cloud-resolving (1km) model treated as “truth”.
PDFs are constrained such that parametrised tendencies based on coarse-grain input fields lie within boxes of width 6K/day.
st.dev.= 22.1 K/day st.dev.= 38.9 K/day
Moderately convecting
Strongly convecting
Weakly convecting
st.dev.= 16.78 K/day
Width of pdf parametrised tendency
Shutts and Palmer, J.Clim, 1987
From Schertzer and Lovejoy, 1993
A stochastic-dynamic paradigm for a Probabilistic Earth-System Model
Computationally-cheap nonlinear stochastic-dynamic models (potentially on a secondary grid) providing specific realisations of sub-grid motions rather than sub-grid bulk effects.
Potentially Coupled over a range of scales
Increasing scale
(Palmer, 1997; 2001)
Examples :
•Multiplicative Noise (Stochastically Perturbed Parametriatsion
Tendencies; SPPT - Buizza et al, 1999)•Stochastic Backscatter (Stochastic Spectral Backscatter Scheme;
SPBS, Shutts, 2005, Berner et al 2010)•Cellular Automata (Palmer 1997, Berner et al 2010)•Stochastic lattice models (Majda et al, 2010)•Dual grid, stochastic mode reduction (Majda et al, 2010: Allen
et al, 2010)•Statistical mechanics of finite sized cloud ensembles (Plant and Craig 2008)•(Perturbed Parameters; Stainforth et al, Smith et al)•(Superparametrisation; Randall et al, 2003)
Why does stochastic-dynamic parametrisation make sense? Here are 5 reasons..
1. As a new approach to reducing model biases
Lenny Smith, personal communication
Surface Pressure
Potential Vorticity on 315K
Persistent Blocking
Anticyclone
Blocking frequency in DEMETER hindcasts
November start, 1959-2001, 9-member ensembles
January (third month)
ERA40 Single models
CNRM ECMWF Met Office
“The mechanisms for atmospheric blocking are only partially understood, but it is clear that there are complex motions, involving meso-scale atmospheric turbulence, and interactions that climate-resolution models may not
be able to represent fully.”
“In developing the UKCP09 projections it was decided not to include probabilistic projections for future wind
due to the high level of associated uncertainty.”
From UKCP09
Will future UK offshore winds be strong enough to provide projected energy needs from
renewables?
We don’t know!
Strong noise
Eg ball bearing in potential well.
Stochastic parametrisation has potential to alter the
mean state of the (nonlinear) model.
Weak noise
Strong noise
-10
-6
-6
-6
-6
-2
-2
-2
-2
-2
-2
-2
-2
-2
2
2
2
2
2
2
6
66
Z500 Difference eto4-er40 (12-3 1990-2005)
-14
-12
-10
-8
-6
-4
-22
4
6
8
10
12
14
-2
-2
-2
-2
2
2
2
2
2
Z500 Difference ezeu-eto4 (12-3 1990-2005)
-14
-12
-10
-8
-6
-4
-22
4
6
8
10
12
14
-2
-2
2
2
2
2
2
2
22
2
6
Z500 Difference eut3-eto4 (12-3 1990-2005)
-14
-12
-10
-8
-6
-4
-22
4
6
8
10
12
14
CNTT95-ERA40 SPBST95-CNTT95CNTT511-CNTT95
T511 T95+Stochastic parametrisation
T95
• Experiments with model cycle 31R1• Experiments with Berner et al (JAS 2009) stochastic
backscatter scheme• Winters (Dec-Mar) of the period 1990-2005
2. As a new approach to representing model uncertainty in ensemble forecasting
Atmosphere Atmosphere Atmosphere Atmosphere Atmosphere Atmosphere
Land surfaceLand surfaceLand surfaceLand surfaceLand surface
Ocean & sea-ice Ocean & sea-ice Ocean & sea-ice Ocean & sea-ice
Sulphateaerosol
Sulphateaerosol
Sulphateaerosol
Non-sulphateaerosol
Non-sulphateaerosol
Carbon cycle Carbon cycle
Atmosphericchemistry
Ocean & sea-icemodel
Sulphurcycle model
Non-sulphateaerosols
Carboncycle model
Land carboncycle model
Ocean carboncycle model
Atmosphericchemistry
Atmosphericchemistry
Off-linemodeldevelopment
Strengthening coloursdenote improvementsin models
1975 1985 1992 1997
The
Met
.Offi
ce H
adle
y C
entr
e
Towards Comprehensive Earth System Models
1970 2000
Atmosphere Atmosphere Atmosphere Atmosphere Atmosphere Atmosphere
Land surfaceLand surfaceLand surfaceLand surfaceLand surface
Ocean & sea-ice Ocean & sea-ice Ocean & sea-ice Ocean & sea-ice
Sulphateaerosol
Sulphateaerosol
Sulphateaerosol
Non-sulphateaerosol
Non-sulphateaerosol
Carbon cycle Carbon cycle
Atmosphericchemistry
Ocean & sea-icemodel
Sulphurcycle model
Non-sulphateaerosols
Carboncycle model
Land carboncycle model
Ocean carboncycle model
Atmosphericchemistry
Atmosphericchemistry
Off-linemodeldevelopment
Strengthening coloursdenote improvementsin models
1975 1985 1992 1997
The
Met
.Offi
ce H
adle
y C
entr
e
1970 2000
Uncertainty
A Missing Box
Multi-model ensemble
In ENSEMBLES the relative ability of these different representations of uncertainty has been tested:Multi-model ensemblesPerturbed parametersStochastic parametrisation (SPPT+SPBS)by making probabilistic seasonal climate predictions.
“Giorgi” Regions
dry wet dry wetAustralia
1 2 2 3MM best 20 24%
Amazon Basin3 0 6 6
PP best 18 21%Southern South America
1 1 1 1SP best 38 45%
Central America2 3 3 2
no SP best 8 10%Western North America
3 3 6 384
Central North America6 1 3 3
Eastern North America1 1 2 3
Alaska3 1 2 3
Greenland1 6 2 3
Mediterranean3 3 3 3
Northern Europe2 2 3 3
Western Africa3 1 2 3
Eastern Africa3 3 2 2
Southern Africa3 3 3 2
Sahel1 3 2 6
South East Asia1 1 1 1
East Asia3 3 3 3
South Asia3 3 3 3
Central Asia2 3 2 2
Tibet1 1 6 6
North Asia3 2 1 1
precipitationJJA DJF
Comparison of the BSS(∞) for precipitation over land regions:ENSEMBLES multi-model ensemble (MM), perturbed parameter ensemble (PP),
ECMWF stochastic physics ensemble (SP) and ECMWF control ensemble (noSP)
lead time: 2-4 months, hindcast period: 1991-2005SP version 1055m007
A Weisheimer, Work in progress
cold warm cold warmAustralia
3 3 3 1MM best 32 38%
Amazon Basin3 1 1 1
PP best 19 23%Southern South America
1 1 3 2SP best 25 30%
Central America3 1 3 1
no SP best 8 10%Western North America
1 1 6 684
Central North America1 1 2 2
Eastern North America3 3 2 3
Alaska3 3 2 2
Greenland1 1 2 2
Mediterranean3 6 1 6
Northern Europe2 2 3 3
Western Africa1 1 3 3
Eastern Africa1 1 2 3
Southern Africa1 2 1 1
Sahel1 2 6 6
South East Asia1 1 2 1
East Asia3 2 1 6
South Asia3 1 3 3
Central Asia1 2 3 2
Tibet3 1 3 6
North Asia1 2 1 2
temperatureJJA DJF
Comparison of the BSS(∞) for temperature over land regions:ENSEMBLES multi-model ensemble (MM), perturbed parameter ensemble (PP),
ECMWF stochastic physics ensemble (SP) and ECMWF control ensemble (noSP)
lead time: 2-4 months, hindcast period: 1991-2005SP version 1055m007
3. As a way to make more efficient use of human and computer resources
Atmosphere Atmosphere Atmosphere Atmosphere Atmosphere Atmosphere
Land surfaceLand surfaceLand surfaceLand surfaceLand surface
Ocean & sea-ice Ocean & sea-ice Ocean & sea-ice Ocean & sea-ice
Sulphateaerosol
Sulphateaerosol
Sulphateaerosol
Non-sulphateaerosol
Non-sulphateaerosol
Carbon cycle Carbon cycle
Atmosphericchemistry
Ocean & sea-icemodel
Sulphurcycle model
Non-sulphateaerosols
Carboncycle model
Land carboncycle model
Ocean carboncycle model
Atmosphericchemistry
Atmosphericchemistry
Off-linemodeldevelopment
Strengthening coloursdenote improvementsin models
1975 1985 1992 1997
The
Met
.Offi
ce H
adle
y C
entr
e
Towards Comprehensive Earth System Models
1970 2000
A community-wide approach to the Climate Model development?
Standard argument against the “Airbus” paradigm:
“We need model diversity in order to be able to estimate prediction uncertainty”
However, development of a skilful Probabilistic Climate Model weakens this argument, opening the door to greater integration of climate model development, and to much more efficient use of the enormous human and computational resources needed to develop reliable climate prediction models.
4. Emerging Probabilistic Computer Hardware?
A New type of chip: PCMOS (Probabilistic Complementary
Metal-Oxide Semiconductor)
Krishna Palem – Rice University
News: AnnouncementsMIT Spin-out Lyric Semiconductor Launches a New Kind of Computing with Probability Processing CircuitsBreakthrough Error Correction for Flash Memories Now Available; Future Technology to Enable 1,000X Performance Over Today’s Digital ProcessorsSANTA CLARA, Calif., and AUSTIN, Texas – August 17, 2010 – FLASH MEMORY SUMMIT and THE INTERNATIONAL SYMPOSIUM ON LOW POWER ELECTRONICS AND DESIGN – Lyric Semiconductor, Inc. a DARPA- and venture-funded MIT spin-out, today emerged from stealth mode to launch a new technology called probability processing, which is poised to deliver a fundamental change in processing performance and power consumption. With over a decade of development at MIT and at Lyric Semiconductor, Lyric’s probability processing technology calculates in a completely new way, enabling orders-of-magnitude improvement in processor efficiency. Lyric Error Correction (LEC™) for flash memory, the first commercial application of probability processing, offers a 30X reduction in die size and a 12X improvement in power consumption all at higher throughput compared to today’s digital solutions. Lyric Semiconductor has developed an alternative to digital computing. The company is redesigning processing circuits from the ground up to natively process probabilities – from the gate circuits to the processor architecture to the programming language. As a result, many applications that today require a thousand conventional processors will soon run in just one Lyric processor, providing 1,000X efficiencies in cost, power, and size.For over 60 years, computers have been based on digital computing principles. Data is represented as bits (1s and 0s). Boolean logic gates perform operations on these bits. Lyric has invented a new kind of logic gate circuit that uses transistors as dimmer switches instead of as on/off switches. These circuits can accept inputs and calculate outputs that are between 0 and 1, directly representing probabilities - levels of certainty.
5. Cos the boss said so!
“I believe that the ultimate climate models..will be stochastic, ie random numbers will appear somewhere in the time derivatives” Lorenz 1975.
Where are we now with Stochastic-Dynamic Parametrisation?
• Atmosphere Partially (SPPT, SPBS)
• Land surface No
• Ocean No
• Cryosphere No
• Biosphere No
3/2 1/2
Let the time it could take some at wavenumber 2
to infect wavenumber , be proportional
to the eddy turn over time ( ) (
ro
)
er r k
k
k k E k
0
The time it could take for to propagate N "octaves"
to some large-scale wavenmber of interest is
( )
erro
)
r
(2
L
Nn
Ln
k
N k
5/3 2/3
0
2 /3
0
If ( ) then ( ) and
( ) (2 )
( ) 2 ( ) as
Nn
Ln
Nn
L Ln
E k k k k
N k
k k N
Hence scaling suggests it could take a finite time for small-scale truncation/parametrisation errors to infect any large scale of interest, no
matter how small-scale these uncertainties are confined to.
Clay Mathematics Millenium Problems
• Birch and Swinnerton-Dyer Conjecture
• Hodge Conjecture
• Navier-Stokes Equations
• P vs NP
• Poincaré Conjecture
• Riemann Hypothesis
• Yang-Mills Theory
The Very Grand Challenge
Mathematicians (the academic community more generally) to help
develop a new generation of ab initio Earth System Models, replacing the
conventional bulk-formula parametrisation paradigm with innovative stochastic-dynamic
mathematics, to aid our ability to predict climate, for the good of society
worldwide.
The tools we have to work with:
• Observations
• Cloud resolving models (coarse grain budgets)
• Physics, mathematics and the power of pure reason!
The Very Grand Challenge
Mathematicians (the academic community more generally) to help
develop a new generation of ab initio Earth System Models, replacing the
conventional bulk-formula parametrisation paradigm with innovative stochastic-dynamic
mathematics, to aid our ability to predict climate, for the good of society
worldwide.